Hard-sphere calculations

Current methods take root in the early 1960s, when the conformational analysis of macromolecules became of general interest [29-30]. Anderson et al. [31] used model building and X-ray diffraction studies to determine the double helical structures of polysaccharides using crystalline structure data as an initial set of coordinates followed by computational sampling of new structures by rotation around selected covalent bonds. The details of these so-called hard-sphere calculations are described in Rees and Skerrett [32] and Rees and Smith [33]. This approach was also applied to carbohydrate conformations in the analysis of bacteria and polysaccharidic structures and linkages [34-35]. 

Lemieux and Koto (1 ) assessed the non-bonded interactions by hard-sphere calculations which are present in the cyclohexyl-type... 

As seen from Figure 1, the hard-sphere calculations infer a much different situation for the 2,6-dimethyl cyclohexyl a-D-glucopyranoside (8) than for the B-anomer (9). For the a-anomer, the ipH torsion angle which provides the minimum energy calculated with <(>H = -60° has near 6 kcal/mole of net destabilizing non-bonded interactions whereas that with -30° involves only about 1 kcal/mole of such interactions. Therefore, based on these calculations, it could be expected that unless the exo-anomeric... 

Figure I. Nonbonded interactions estimated by hard-sphere calculations (1) to be present in the substituted cyclohexyl a- and fi-D-glycopyranosides (Compounds 4 to 9) as a function of the H torsion angle. The point for a specific H angle corresponds to the conformation for which the H angle provided the minimum...

A Comparison of Solid-Fluid Coexistence Properties for Hard Spheres Calculated via Various Theories with Results from Computer Simulation. Values of the Lindemann Parameter, L, for the Melting Solid are also Given... 

The column headed HSE uses an approximation made originally by Mansoori and Leland (3) that the diameter used in the hard sphere equations of state is c0o-, the LJ a parameter for each molecule multiplied by a universal constant for conformal fluids. This approximation then requires that be replaced by equations defining the HSE pseudo parameters, Equations 10 and 11. The results in the HSE column use c0 = 0.98, the value for LJ fluids obtained empirically by Mansoori and Leland. This procedure is correct only for a Kihara-type potential and it is not consistent with the LJ fluids in Table I. Furthermore, this causes only the high temperature limit of the repulsion effects to be included in the hard-sphere calculation. Soft repulsions are predicted by the reference fluid. 

Figure 6 shows our PRISM theory predictions for g(r) of polyethylene at 430 K and three different densities using d = 3.% A for the hard core diameter. Note that g(r) for polyethylene is somewhat more complex than in the tangent hard sphere calculations in Figs. 2 due to the multiplicity of length scales (i.e. d The first peak, which occurs at the hard core diameter for tangent... 

Fig. 118. A comparison of the Camahan-Starling approximation with the Ree and Hoover hard sphere calculation.

Figure 6 Comparison of the form factor of a star polymer with 128 arms with the form factor of an equal-density hard sphere calculated by Eq. (29). The radius of the sphere...

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